Each of the seventy-two carries a scriptural verse, and the pairings are among the most confidently reported and least well sourced features of the system.
The tradition states a rule of letter-correspondence: the verse is one in which the letters of the angel's three-letter root can be found, so that name and verse confirm one another. Different sources state the rule differently, initial letters of words, letters anywhere in the verse, the first and last letters, and the versions are not equivalent. Applied to the lists as printed, none of them holds throughout.
Several other observations bear on the question.
The verses are overwhelmingly from the Psalms, which is where the tradition looked for material of this kind, and they are cited by the numbering used in Christian Bibles rather than the Hebrew, where the Psalms are numbered and versified somewhat differently. That alone dates the pairing as it now circulates to a Christian context.
At least one entry in the standard list is not a psalm at all. The seventieth is assigned Genesis 1:1, the opening of the creation account. Whatever rule governed the selection, either it admitted exceptions or the exception was introduced later for a reason not recorded.
And the pairings are not attested in the medieval Jewish sources that describe the derivation. Rashi gives the technique; he does not give verses. The pairing in its familiar form belongs to the early modern and nineteenth-century literature, Lenain's 1823 tabulation prominent among them.
The verses are therefore best described as a traditional apparatus of documented but late origin, assembled by a rule that the tradition states and the lists do not consistently obey.